The purpose of this paper is to make up for lacks of the past researches with respect to basic search models with continuous effort. We suppose a discrete search space composed of n boxes and an exponential-type deteetion function in each box, First an explicit solution is derived fbr a detection search game. Secondly we consider an inforrnation search problern and propose a sequential method of constructing the optimal policy. Thirdly we consider a certainty search game in which the payoff function is given by the posterior uncertainty with respecl/ to the position of player I (hideD and obtain the solution in the form ofa solution of a certain simultaneous equations. Finally we consider a whereabouts search model and derive the sarne result as the discrete effbrt case.
We consider a non-zero-sum game in which two searchers (player I and II) compete with each other for quicker detection of an object hidden in one of n boxes. Let p (q) be the prior location distribution of the object for player I (II). Exponential detection functions are assumed for both players. Each player wishes to maximize the probability that he detects the object before the opponent detects it. In the general case, a Nash equilibrium point is obtained in the form of a solution of simultaneous differential equations. In the case of p = q, we obtain an explicit solution showing the surprising result that both players have the same equilibrium strategy even though the detection rates are different.
We consider a non-zero-sum game in which two searchers (player I and II) compete with each other for quicker detection of an object hidden in one of n boxes. Let p (q) be the prior location distribution of the object for player I (II). Exponential detection functions are assumed for both players. Each player wishes to maximize the probability that he detects the object before the opponent detects it. In the general case, a Nash equilibrium point is obtained in the form of a solution of simultaneous differential equations. In the case of p = q, we obtain an explicit solution showing the surprising result that both players have the same equilibrium strategy even though the detection rates are different.
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